electricity generation using kites

14
1066-033X/07/$25.00©2007IEEE DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 25 Power Kites for Wind Energy Generation Fast Predictive Control of Tethered Airfoils BY MASSIMO CANALE, LORENZO FAGIANO, and MARIO MILANESE T he problems posed by electric energy generation from fossil sources include high costs due to large demand and limited resources, pollution and CO 2 production, and the geopolitics of producer countries. These problems can be overcome by alternative sources that are renewable, cheap, easily available, and sustainable. However, current renewable technologies have limitations. Indeed, even the most optimistic forecast on the diffusion of wind, photo- voltaic, and biomass sources estimates no more than a 20% contribution to total energy production within the next 15–20 years. Excluding hydropower plants, wind turbines are cur- rently the largest source of renewable energy [1]. Unfortu- nately, wind turbines require heavy towers, foundations, and huge blades, which impact the environment in terms of land usage and noise generated by blade rotation, and require massive investments with long-term amortization. Consequently, electric energy production costs are not yet competitive with thermal generators, despite recent increases in oil and gas prices. Digital Object Identifier 10.1109/MCS.2007.909465

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Page 1: Electricity Generation Using Kites

1066-033X/07/$25.00©2007IEEE DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 25

FUTURE DIRECTIONSTire modeling and tire parameter estimation are need-ed to reduce the cost of direct TPMSs and to overcomethe shortcomings of indirect TPMSs. A classical solu-tion is to model the dependence of tire/road friction ontire pressure, which can then be extracted from the fric-tion coefficient. Alternatively, one can consider addi-tional factors that affect tire inflation pressure, such asvertical force and vertical deflection [4]. A combinationof tire speed and tire height can estimate inflation moreprecisely than current indirect TPMSs. This approachneeds an additional height sensor or accelerometer,which is available in vehicles with semi-active or activesuspensions.

Yet another approach relies on the fact that the reso-nance frequency of the tire changes with respect to pres-sure [5], [6], as modeled by

ωresonance ∼=√

m,

where k denotes tire stiffness, �k denotes change in tirestiffness, and m denotes mass acting on the tire. If thetire pressure changes, then the spring constant changes,resulting in a change in the natural frequency. Thewheel vibration can be measured either by the tirespeed or through an accelerometer. Alternatively, tireinflation can be identified through nonlinear identifica-tion techniques, which rely on tire stiffness changeswith respect to pressure [7].

Due to the U.S. law mandating direct TPMSs, sensorindustries are interested in producing cost-effective solu-tions. While promising theoretical and practical results[4]–[7] are available for indirect TPMSs, they have not yetappeared in commercial products.

REFERENCES[1] L. Wingert, Not to Air Is human. Crane Communications, 2000.[2] N. Normann, Tyre Pressure Monitoring System for all Vehicle Categories.Crane Communications Inc.: ATZ Worldwide, 2000.[3] NHTSA, Federal Motor Vehicle Safety Standards [Online]. Available:http://www.nhtsa.dot.gov/cars/rules[4] H. Shraim, A. Rabhi, M. Ouladsine, N.K. M’Sirid, and L. Fridman, “Esti-mation and analysis of the tire pressure effects on the comportment of thevehicle center of gravity},” in Proc. 9th Int. Workshop on Variable Structure Sys-tems, Italy), June 2006, pp. 268–273.[5] L. Li, F.-Y. Wang, Q. Zhou, and G. Shan, “Automatic tire pressure faultmonitor using wavelet-based probability density estimation,” in Proc. IEEEIntelligent Vehicle Symp., June 2003, pp. 80–84.[6] N. Persson, F. Gustafsson, and M. Drevö, “Indirect tire pressure monitoringusing sensor fusion,” in Proc. SAE 2002, Detroit, June 2002, no. 2002-01-1250.[7] C.R. Carlson and J.C. Gerdes, “Identifying tire pressure variation by non-linear estimation of longitudinal stiffness and effective radius,” in Proc.AVEC2002, Japan, 2002.

AUTHOR INFORMATIONV. Sankaranarayanan ([email protected]) received thePh.D. degree in systems and control engineering from IIT-Bombay in 2006. He is currently a postdoctoral researcher inthe Mechanical Engineering Department at Istanbul Techni-cal University. His research interests include nonlinear con-trol, underactuated systems, sliding mode control, andautomotive control systems.

Levent Güvenç received the B.S. degree in mechanicalengineering from Bogaziçi University, Istanbul, in 1985,the M.S. degree in mechanical engineering from ClemsonUniversity in 1988, and the Ph.D. degree in mechanicalengineering from the Ohio State University in 1992. Since1996, he has been a faculty member in the MechanicalEngineering Department of Istanbul Technical University,where he is currently a professor of mechanical engineer-ing and director of the Mechatronics Research Lab and theEU-funded Automotive Controls and MechatronicsResearch Center. His research interests include automotivecontrol mechatronics, helicopter stability and control, andapplied robust control.

Power Kites for Wind Energy GenerationFast Predictive Control of Tethered Airfoils

BY MASSIMO CANALE, LORENZO FAGIANO, and MARIO MILANESE

The problems posed by electric energy generation fromfossil sources include high costs due to large demandand limited resources, pollution and CO2 production,

and the geopolitics of producer countries. These problemscan be overcome by alternative sources that are renewable,cheap, easily available, and sustainable. However, currentrenewable technologies have limitations. Indeed, even themost optimistic forecast on the diffusion of wind, photo-voltaic, and biomass sources estimates no more than a 20%

contribution to total energy production within the next15–20 years.

Excluding hydropower plants, wind turbines are cur-rently the largest source of renewable energy [1]. Unfortu-nately, wind turbines require heavy towers, foundations,and huge blades, which impact the environment in termsof land usage and noise generated by blade rotation, andrequire massive investments with long-term amortization.Consequently, electric energy production costs are not yetcompetitive with thermal generators, despite recentincreases in oil and gas prices.Digital Object Identifier 10.1109/MCS.2007.909465

Page 2: Electricity Generation Using Kites

THE KITEGEN PROJECTTo overcome the limitations of current wind power tech-nology, the KiteGen project was initiated at Politecnico diTorino to design and build a new class of wind energygenerators in collaboration with Sequoia Automation,Modelway, and Centro Studi Industriali. The project focus[2], [3] is to capture wind energy by means of controlledtethered airfoils, that is, kites; see Figure 1.

The KiteGen project has designed and simulated asmall-scale prototype (see Figure 2). The two kite lines arerolled around two drums and linked to two electric drives,which are fixed to the ground. The flight of the kite is con-trolled by regulating the pulling force on each line. Energyis collected when the wind force on the kite unrolls thelines, and the electric drives act as generators due to therotation of the drums. When the maximal line length ofabout 300 m is reached, the drives act as motors to recoverthe kite, spending a small percentage (about 12%, see the“Simulation Results” section for details) of the previously

generated energy [4]. This yo-yo configuration is under thecontrol of the kite steering unit (KSU, see Figure 3), whichincludes the electric drives (for a total power of 40 kW), thedrums, and all of the hardware needed to control a singlekite. The aims of the prototype are to demonstrate the abil-ity to control the flight of a single kite, to produce a signifi-cant amount of energy, and to verify the energyproduction levels predicted in simulation studies.

The potential of a similar yo-yo configuration is investi-gated, by means of simulation results, in [5] and [6] for oneor more kites linked to a single cable. In [5] and [6], it isassumed that the angle of incidence of the kites can becontrolled. Thus, the control inputs are not only the rollangle ψ and the cable winding speed, as considered in [4]and in this article, but also the lift coefficient CL.

For medium-to-large-scale energy generators, an alter-native KiteGen configuration is being studied, namely, thecarousel configuration. In this configuration, introduced in[7] and shown in Figure 4, several airfoils are controlled by

their KSUs placed on the arms of a verti-cal-axis rotor. The controller of each kite isdesigned to maximize the torque exertedon the rotor, which transmits its motion toan electric generator. For a given winddirection, each airfoil can produce energyfor about 300◦ of carousel rotation; only asmall fraction (about 1%, see the “Simula-tion Results” section for details) of thegenerated energy is used to drag the kiteagainst the wind for the remaining 60◦.

According to our simulation results, itis estimated that the required land usagefor a kite generator may be lower than acurrent wind farm of the same power by afactor of up to 30–50, with electric energy

FIGURE 1 Kite surfing. Expert kite-surfers drive kites to obtain ener-gy for propulsion. Control technology can be applied to exploit thistechnique for electric energy generation.

FIGURE 2 KiteGen small-scale prototype of a yo-yo configuration.The kite lines are linked to two electric drives. The flight of the kite iscontrolled by regulating the pulling force on each line, and energy isgenerated as the kite unrolls the lines.

FIGURE 3 Scheme of the kite steering unit. The kite steering unit, which provides auto-matic control for KiteGen, includes the electric drives, drums, and all of the hardwareneeded to control a single kite.

Onboard Sensors(Kite Position and Speed)

Lines

Actuation Unit(Electric Drives and Winches)

KiteW

1

6 5

76

3

4

2

ControlSoftware

Ground Sensors(Wind Speed and Direction,Line Strength)

26 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007

Page 3: Electricity Generation Using Kites

production costs lower by a factor up to 10–20. Such poten-tial improvement over current wind technology is due toseveral aerodynamic and mechanical reasons [8], [9]. Forexample, 90% of the power generated by a 2-MW three-blade turbine with a 90-m rotor diameter is contributed byonly the outer 40% of the blade area, corresponding toabout 120 m2. This dependence is due to the fact that theaerodynamic forces on each infinitesimal section of theblades are proportional to the square of its speed withrespect to the air, and this speed increases toward the tip ofthe blades. In KiteGen, the tethered airfoils act as the outerportions of the blades, without the need for mechanicalsupport of the tower and of the less-productive inner bladeportions; see Figure 5. Indeed, a mean generated power of620 kW is obtained in the simulation reported in Figure 16for a single kite of 100-m2 area and 300-m line length.

Figure 5 shows that the torque exerted by wind forces atthe base of a wind turbine’s support structure increases with

FIGURE 4 KiteGen carousel configuration concept. Several airfoilsare controlled by the kite steering units placed on the arms of a ver-tical axis rotor. The airfoils’ flight is controlled so as to turn the rotor,which transmits its motion to an electric generator.

At present, a small scale yo-yo prototype has been real-

ized (see Figure S1). This system can generate up to

40 kW using commercial kites with characteristic area up to

10 m2 and line length up to 800 m. The prototype is under

test (see Figure S2). Preliminary tests show that the

amount of energy predicted by simulation is confirmed by

experimental data.

A new KiteGen prototype is expected to be built in the

next 24–36 months to demonstrate the energy-generation

capabilities of the carousel configuration. In particular, a

carousel structure with a single kite steering unit mounted

on a cart riding on a circular rail will be considered. To col-

lect the energy produced by the wagon motion, the wheels

of the cart are connected to an alternator. Such a proto-

type is expected to produce about 0.5 MW with a rail

radius of about 300 m. According to scalability, a platoon

of carts, each one equipped with a kite steering unit, can

be mounted on the rail to obtain a more effective wind

power plant. This configuration can generate, on the basis

of preliminary computations, about 100 MW at a produc-

tion cost of about 20 €/MWh, which is two to three times

lower than from fossil sources.

FIGURE S1 The first KiteGen prototype. Based on the yo-yo con-figuration, KiteGen can generate up to 40 kW using commercialkites with characteristic area up to 10 m2 and line length up to800 m. Preliminary tests show that the amount of energy predict-ed by simulation is confirmed by experimental data. A new Kite-Gen prototype is expected to be built in the next 24 to 36 monthsto demonstrate energy-generation capabilities of the carouselconfiguration.

FIGURE S2 KiteGen small scale prototype flying tests. This pic-ture shows the kite motion and line developing during the trac-tion phase. The kite steering unit is mounted on a light truck foreasy transportation to locations with favorable wind conditions.This picture was taken on a hill near Torino.

KiteGen Project Perspectives

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 27

Page 4: Electricity Generation Using Kites

the height of the tower, the force is independent of the linelength in KiteGen. Due to structural and economical limits, itis not convenient to go beyond the 100–120 m height of thelargest turbines commercially available. In contrast, airfoilscan fly at altitudes up to several hundred meters, takingadvantage of the fact that, as altitude over the ground increas-es, the wind is faster and less variable; see Figure 6. For exam-ple, at 800 m the mean wind speed doubles with respect to 100m (the altitude at which the largest wind turbines operate).Since the power that can be extracted from wind grows withthe cube of the wind speed, the possibility of reaching suchheights represents a further significant advantage of KiteGen.

The carousel configuration is scalable up to severalhundred megawatts, leading to increasing advantagesover current wind farms. Using data from the Danish

Wind Industry Association Web site [10], it follows that,for a site such as Brindisi, in the south of Italy, a 2-MWwind turbine has a mean production of 4000 MWh/year.To attain a mean generation of 9 TWh/year, which corre-sponds to almost 1000-MW mean power, 2250 such towersare required, with a land usage of 300 km2 and an energyproduction cost of about 100–120 €/MWh. In comparison,the production cost from fossil sources (gas, oil) is about60–70 €/MWh. Simulation results show that a KiteGencapable of generating the same mean energy can berealized using 60–70 airfoils of about 500 m2, rotating in acarousel configuration of 1500-m radius and flying up to800 m. The resulting land usage is 8 km2, and the energyproduction cost is estimated to be about 10–15 €/MWh.

SYSTEM AND CONTROL TECHNOLOGIES NEEDED FOR KITEGEN

Control DesignThe main objective of KiteGen control is to maximize energygeneration while preventing the airfoils from falling to theground or the lines from tangling. The control problem canbe expressed in terms of maximizing a cost function that pre-dicts the net energy generation while satisfying constraintson the input and state variables. Nonlinear model predictivecontrol (MPC) [11] is employed to accomplish these objec-tives, since it aims to optimize a given cost function and fulfillconstraints at the same time. However, fast implementation isneeded to allow real-time control at the required samplingtime, which is on the order of 0.1 s. In particular, the imple-mentation of fast model predictive control (FMPC) based onset membership approximation methodologies as in [12] and[13] is adopted, see “How Does FMPC Work ?” for details.

Model IdentificationOptimizing performance for Kite-Gen relies on predicting the behav-ior of the system dynamics asaccurately as possible. However,since accurately modeling thedynamics of a nonrigid airfoil ischallenging, model-based controldesign may not perform satisfacto-rily on the real system. In this case,methods for identifying nonlinearsystems [14], [15] can be applied toderive more accurate models.

Sensors and Sensor FusionThe KiteGen controller is based onfeedback of the kite position andspeed vector, which must be mea-sured or accurately estimated. Eachairfoil is thus equipped with a pairof triaxial accelerometers and a pair

FIGURE 5 Comparison between wind turbines and airfoils in energyproduction. In wind towers, limited blade portions (red) contributepredominantly to power production. In KiteGen, the kite acts as themost active portions of the blades, without the need for mechanicalsupport of the less active portions and the tower.

Forces Exerted by Wind

Wind Tower KiteGen

FIGURE 6 Wind-speed variation as a function of altitude. These data are based on the averageEuropean wind speed of 3 m/s at ground level. Source: Delft University, Dr. Wubbo Ockels.

Alti

tude

(m

)

3,0002,8002,6002,4002,2002,0001,8001,6001,4001,2001,000

800600400200

0

Wind Speed (m/s)

3 5 7 9 11 13 15

28 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007

Page 5: Electricity Generation Using Kites

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 29

The fast model predictive control (FMPC) approach intro-

duced and described in [12] and [13] is based on set mem-

bership techniques. The main idea is to find a function f that

approximates the exact predictive control law ψ(tk) = f (w(tk))

to a specified accuracy. Evaluating the approximating function

is faster than solving the constrained optimization problem con-

sidered in MPC design.

To be more specific, consider a bounded region W ⊂ R8

where w can evolve. The region W can be sampled by choosing

wk ∈ W, k = 1, . . . , ν , and computing offline the corresponding

exact MPC control given by

ψk = f (wk), k = 1, . . . , ν. (S1)

The aim is to derive, from these known values of ψk and wk

and from known properties of f , an approximation f of f over

W, along with a measure of the approximation error. Neural

networks are used in [S1] for such an approximation. However,

neural networks have limitations, such as the possibility of

local minima during the learning phase and the difficulty of sat-

isfying the constraints in the image set of the function to be

approximated. Moreover, no measure of the approximation

error is provided. To overcome these drawbacks, a set mem-

bership approach is used in [12] for MPC with linear models.

Based on sampled data and a priori information about f , the

approach finds a feasible function set in which the true function

is guaranteed to lie. An optimal approximation, along with

approximation error, is derived based on this set. In the case of

KiteGen control it is assumed that f ∈ Fγ , where Fγ is the set

of Lipschitz functions on W with Lipschitz constant γ . Note that

stronger assumptions cannot be made, since even in the sim-

ple case of linear dynamics and a quadratic functional, f is a

piecewise linear continuous function [S2]. In addition, the input

saturation condition gives the a priori bound | f (w)| ≤ ψ . This

information about the function f , combined with the values of

the function at the points wk ∈ W, k = 1, . . . , ν , implies that f

is a member of the feasible function set

FFS = {f ∈ Fγ : |f (w)| ≤ ψ; f (wk ) = ψk , k = 1, . . . , ν},(S2)

which summarizes the available information on f . Set membership

theory facilitates the derivation of an optimal estimate of f and its

approximation error in terms of the L p(W) norm for p ∈ [1,∞],

where || f ||p.= [

∫W | f (wt)|pdw ]

1p , p ∈ [1,∞), and || f ||∞ .= ess-

supw∈W

| f (w)|. For given f ≈ f , the related L p approximation error is

‖ f − f ‖p. Since the true function f is known at only a finite numberof points, the error between f and f is unknown. However, given

the a priori information, the tightest guaranteed bound is given by

∥∥∥ f − f∥∥∥

p≤ sup

f ∈F F S

∥∥∥ f − f∥∥∥

p

.= E( f ), (S3)

where E( f ) is the (guaranteed) approximation error.

A function f ∗ is optimal approximation if

r p.= E( f ∗) = inf

fE( f ),

where the radius of information r p gives the minimal Lp approxima-

tion error that can be guaranteed. Defining

f (w).= min

[ψ, min

k=1,...,ν

(ψk + γ ‖w − wk‖

)], (S4)

f (w).= max

[−ψ, max

k=1,...,ν

(ψk − γ ‖w − wk‖

)], (S5)

yields the function

f ∗(w) = 12

[ f (w) + f (w)], (S6)

which is an optimal approximation in the L p(W) norm for all

p ∈ [1,∞] [13]. Moreover, the approximation error of f ∗ is point-

wise bounded as

|f (w) − f ∗(w)| ≤ 12

|f (w) − f (w)|, for all w ∈ W

and is pointwise convergent to zero [13]

limν→∞ |f (w) − f ∗(w)| = 0, for all w ∈ W, (S7)

Thus, evaluating supw∈W

| f (w) − f (w)|, it is possible to decide

whether the values of w1, . . . , wν , chosen for the offline compu-

tation of ψk are sufficient to achieve a desired accuracy in the

estimation of f or if the value of ν must be increased. Then, the

MPC control can be approximately implemented online by evalu-

ating the function f ∗(wtk) at each sampling time so that

ψtk = f ∗(wtk).

As ν increases, the approximation error decreases at the cost of

increased computation time.

REFERENCES

[S1] T. Parisini and R. Zoppoli, “A receding-horizon regulator for

nonlinear systems and a neural approximation,” Automatica, vol.

31, no. 10, pp. 1443–1451, 1995.

[S2] A. Bemporad, M. Morari, V. Dua, and E.N. Pistikopoulos “The

explicit linear quadratic regulator for constrained systems,” Auto-

matica, vol. 38, pp. 3–20, 2002

How Does FMPC Work?

Page 6: Electricity Generation Using Kites

of triaxial magnetometers placed at the airfoil’s extremeedges, which transmit data to the control unit by means ofradio signals. These data are sufficient for estimating thekite position and speed. However, in order to improve esti-mation accuracy and to achieve some degree of recovery inthe case of sensor failure, we plan to use a load cell to mea-sure the length and traction force of each line as well as avision system to determine the kite angular position.

A key issue in KiteGen operation is the detection andrecovery of possible breakdowns or malfunctions of thesensors. For example, the vision system may not operate inthe presence of clouds, haze, or heavy rain. A commonway to treat this problem is to use estimation techniquesbased on the system model and available measurements.However, due to the kite’s nonlinear dynamics, theextended Kalman filter (EKF), based on approximations ofthe nonlinearities, gives rise to numerical stability prob-lems and severe accuracy deterioration. Moreover, the EKFdesign is based on a model that, although quite complexand nonlinear, is only an approximate description of theactual system. Alternatively, the direct virtual sensor(DVS) approach [16], [17] facilitates the design of an opti-mal filter based on experimental data collected in theabsence of sensor faults. In particular, when an accuratemodel is available and the noise statistical hypotheses are

fulfilled, the DVS gives the same accuracy as the theoreti-cal minimal variance filter. Moreover, in the presence ofmodeling errors and nonlinearities, the DVS guaranteesstability and performs tradeoffs between optimality androbustness, which are not achievable with EKF.

KITE GENERATOR MODELS

Kite DynamicsThe model developed in [18] describes the kite dynamics.A fixed cartesian coordinate system (X, Y, Z) is considered(see Figure 7), with the X axis aligned with the nominalwind speed vector. The wind speed vector is representedas �Wl = �W0 + �Wt, where �W0 is the nominal wind, assumedto be known and expressed in (X, Y, Z) as

�W0 =⎛⎝ Wx(Z)

00

⎞⎠ , (1)

where Wx(Z) is a known function that gives the windnominal speed at each altitude Z (see Figure 6). The term�Wt may have components in all directions and is assumed

to be unknown, accounting for unmeasured turbulence.A second cartesian coordinate system (X′, Y′, Z′), cen-

tered at the KSU location, is introduced to take intoaccount possible KSU motion with respect to (X, Y, Z); oth-erwise, (X′, Y′, Z′) ≡ (X, Y, Z) is assumed. In this system,the kite position can be expressed as a function of its dis-tance r from the origin and the angles θ and φ, as depictedin Figure 7, which also shows the basis vectors eθ , eφ , er ofa local coordinate system centered at the kite location.

Applying Newton’s laws of motion to the kite in thelocal coordinate system yields

θ = Fθ

m r, (2)

φ = Fφ

m rsin θ, (3)

r = Fr

m, (4)

where m is the kite mass, and the forces Fθ , Fφ , and Fr

include the contributions of the gravitational force mg,apparent force �Fapp, aerodynamic force �Faer, and the forceFc exerted by the lines on the kite. Expressed in the localcoordinates, the forces are given by

Fθ = (sin θ)mg + Fapp,θ + Faer,θ , (5)

Fφ = Fapp,φ + Faer,φ , (6)

Fr = −(cos θ)mg + Fapp,r + Faer,r − Fc . (7)

Apparent ForcesThe components of the apparent force vector �Fapp depend onthe kite generator configuration. For example, for the yo-yo

30 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007

FIGURE 7 Model of a single kite steering unit. A fixed cartesian coor-dinate system (X, Y, Z) is considered, with the X axis aligned withthe direction of the nominal wind speed vector �W0. A second carte-sian coordinate system (X ′, Y ′, Z ′), centered at the KSU location,is considered when KSU is moving with respect to (X, Y, Z). In theyo-yo configuration, since the KSU location is fixed at the ground,(X ′, Y ′, Z ′) ≡ (X, Y, Z) is assumed. In the coordinate system(X ′, Y ′, Z ′), the kite position can be expressed as a function of itsdistance r from the origin and of the two angles θ and φ. In thecarousel configuration, the KSU rotates around the origin of(X, Y, Z) at distance R, with angular speed �. The local coordinatesystem (�eθ , �eφ, �er ) is also shown.

er

Z'

φ

θr

X' Y'

R

X

Y

Z

W0

Θ

KSU

Page 7: Electricity Generation Using Kites

configuration, centrifugal inertial forces have to be considered,that is, �Fapp = �Fapp(θ, φ, r, θ , φ, r). For the carousel configura-tion, since each KSU moves along a circular trajectory withconstant radius R (see Figure 7), the carousel rotation angle �and its derivatives must be included in the apparent force cal-culation, so that �Fapp = �Fapp(θ, φ, r,�, θ, φ, r, �, �).

Aerodynamic ForcesThe aerodynamic force �Faer depends on the effective windspeed �We, which in the local system is computed as

�We = �Wa − �Wl, (8)

where �Wa is the kite speed with respect to the ground. Forboth the yo-yo and carousel configurations, �Wa can beexpressed as a function of the local coordinate system(φ, θ, r) and the position of the KSU with respect to thefixed coordinate system (X, Y, Z).

Let us consider now the kite wind coordinate system,with its origin located at the kite center of gravity, the basisvector �xw aligned with the effective wind speed vector, thebasis vector �zw contained by the kite longitudinal plane ofsymmetry and pointing from the top surface of the kite tothe bottom, and the basis vector �yw completing a right-handed system. In the wind coordinate system the aerody-namic force �Faer,w is given by

�Faer,w = FD�xw + FL�zw, (9)

where FD is the drag force and FL is the lift force, comput-ed as

FD = −12

CDAρ|We|2, (10)

FL = −12

CLAρ|We|2, (11)

where ρ is the air density, A is the kite characteristic area,and CL and CD are the kite lift and drag coefficients. All ofthese variables are assumed to be constant. The aerody-namic force �Faer can then be expressed in the local coordi-nate system as a nonlinear function of several argumentsof the form

�Faer =⎛⎝ Faer,θ (θ, φ, r, ψ, �We)

Faer,φ(θ, φ, r, ψ, �We)

Faer,r(θ, φ, r, ψ, �We)

⎞⎠ . (12)

The kite roll angle ψ in (12) is the control variable, defined by

ψ = arcsin(

�ld

), (13)

where d is the kite width and �l is the length differencebetween the two lines (see Figure 8). The roll angle ψ influ-ences the kite motion by changing the direction of �Faer.

Line ForcesConcerning the effect of the lines, the force Fc is alwaysdirected along the local unit vector er and cannot be neg-ative, since the kite can only pull the lines. Moreover, Fc

is measured by a force transducer on the KSU, and,through control of the electric drives, it is regulated sothat the line speed satisfies r(t) ≈ rref(t), where rref(t) ischosen. In the case of the yo-yo configuration,Fc(t) = Fc(θ, φ, r, θ , φ, r, rref, �We) , while, for the carouselconfiguration, Fc(t) = Fc(θ, φ, r,�, θ, φ, r, �, rref, �We).

Motor DynamicsIn the case of the carousel configuration, the motion law forthe generator rotor is taken into account by the equation

Jz� = R Fc(sin θ) sin φ − Tc, (14)

where Jz is the rotor moment of inertia and Tc is the torqueof the electric generator/motor linked to the rotor. Viscousterms are neglected in (14) since the rotor speed � is keptlow as shown in the “Simulation Results” section. Tc ispositive when the kite is pulling the rotor with increasingvalues of �, thus generating energy, and it is negativewhen the electric generator is acting as a motor to drag therotor when the kite is not able to generate a pulling force.The torque Tc is set by a local controller to keep the rotor atconstant speed � = �ref.

KiteGen Dynamics DescriptionThe generic system dynamics are of the form

x(t) = g(x(t), u(t), Wx(t), rref(t), �ref(t), �Wt(t)), (15)

where x(t) = [θ(t) φ(t) r(t) �(t) θ(t) φ(t) r(t) �(t)]T are themodel states and u(t) = ψ(t) is the control variable. In thecase of the yo-yo configuration, � = � = �ref = 0. All ofthe model states are assumed to be measured or estimatedfor use in feedback control. Mechanical power P generated

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 31

FIGURE 8 Forces acting on the kite. The aerodynamic lift and dragforces are FL and FD , respectively, the gravitational force is mg ,and the pulling force Fc is exerted by the lines. The length differencebetween the lines gives the roll input angle ψ .

We FL

FL

Fc mg

FD d Δlψ

Page 8: Electricity Generation Using Kites

with KiteGen is the sum of the power generated byunrolling the lines and the power generated by the rotormovement, that is,

P(t) = r(t)Fc(t) + �(t)Tc(t) . (16)

Both terms in (16) can be negative when the kite lines arebeing recovered in the yo-yo configuration or the rotor isbeing dragged against the wind in the carousel configuration.For the yo-yo configuration the term � Tc is zero, and thusthe generated mechanical energy is due only to line unrolling.Note that (16) is related to a carousel with a single KSU.When more kites are linked to the same carousel, the effect ofline rolling/unrolling for each kite must be included.

KITEGEN CONTROLTo investigate the potential of KiteGen and to assist in thedesign of physical prototypes, a controller is designed foruse in numerical simulations. In particular, the mathemati-cal models of the yo-yo and carousel configurationsdescribed in the section “Kite Generator Models” are usedto design nonlinear model predictive controllers.

In both KiteGen configurations, energy is generated bycontinually performing a two-phase cycle. In the firstphase, the kite exploits wind power to generate mechani-cal energy until a condition is reached that impairs furtherenergy generation. In the second phase, the kite is recov-ered to a suitable position to start another productivephase. These phases are referred to as the traction phase and

passive phase, respectively.Thus, different MPC con-trollers are designed tocontrol the kite in the trac-tion and passive phases.For the overall cycle to beproductive, the totalamount of energy pro-duced in the first phasemust be greater than theenergy spent in the secondphase. Consequently, thecontroller employed in thetraction phase must maxi-mize the produced energy,while the objective of thepassive phase controller isto maneuver the kite tothe traction-phase initialposition with minimalenergy. The main reasonfor using MPC is thatinput and state constraintsmust be imposed, forexample, to keep the kitesufficiently far from the

ground and to account for actuator physical limitations.Moreover, other constraints on the state variables areadded to force the kite to follow figure-eight trajectories toprevent the lines from tangling.

MPC for KiteGenMPC is a model-based control technique that handles bothstate and input constraints. With MPC, the computation ofthe control variable is performed at discrete time instantsdefined on the basis of a suitably chosen sampling period�t. Without wind disturbances, (15) becomes

x(t) = g(x(t), u(t), Wx(t), rref(t), �ref(t)),

where u(t) = ψ(t) is the control variable. At each samplingtime tk = k�t, the measured values of the state x(tk) andthe wind speed Wx(tk), together with the reference speedsrref(tk), �ref(tk) are used to compute the control u(t)through the performance index

J(U, tk, Tp) =∫ tk+Tp

tk

L(x(τ), u(τ), Wx(τ), rref, �ref(τ))dτ ,

(17)

where Tp = Np�t, is the prediction horizon of Np steps,x(τ) is the state predicted inside the prediction horizonaccording to (15) using �Wt(t) = 0 and x(tk) = x(tk), and thepiecewise constant control input u(t) belonging to thesequence U = {u(t)}, t ∈ [tk, tk+Tp] is defined as

32 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007

FIGURE 9 Yo-yo configuration phases. The kite steering unit acts on the kite lines in such a way that ener-gy is generated in the traction phase (green) and spent in the passive phase (red). Each cycle beginswhen the proper starting conditions (circled in blue) are satisfied. In this simulation the effects of turbu-lence are neglected.

020

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Page 9: Electricity Generation Using Kites

u(t) ={ui, for all t ∈ [ti, ti+1], i = k, . . . , k + Tc − 1,

uk+Tc−1, for all t ∈ [ti, ti+1], i = k + Tc, . . . , k + Tp − 1,

(18)

where Tc = Nc�t, and Nc ≤ Np isthe control horizon. The functionL(·) in (17) is defined to maxi-mize the energy generated in thetraction phase and minimize theenergy spent in the passivephase. Moreover, to account forphysical limitations on both thekite behavior and the controlinput ψ , constraints of the formx(t) ∈ X, u(t) ∈ U can be includ-ed. In particular, to keep the kitesufficiently far from the ground,the state constraint

θ(t) ≤ θ

is considered with θ < π/2. Actua-tor physical limitations are takeninto account by the constraints

|ψ(t)| ≤ ψ,

|ψ(t)| ≤ ψ.

Tables 2 and 4 provide detailson the values of ψ and ψ for theyo-yo and carousel configura-tions, respectively. Additionalconstraints are added to forcethe kite to follow figure-eighttrajectories rather than circularones to prevent the tangling ofthe lines. Such constraints forcethe angle φ to oscillate at halfthe frequency of the angle θ ,thus generating the desired kitetrajectory.

The predictive control law,which is computed using areceding horizon strategy, is anonlinear static function of thesystem state x, the nominalmeasured wind speed Wx , andthe reference speeds rref, �ref ofthe form

ψ(tk) = f (x(tk), Wx(tk), rref(tk), �ref(tk)). (19)

Yo-Yo Configuration ControllerThe traction phase begins when the kite is flying in aprescribed zone downwind of the KSU, at a suitablealtitude ZI with a given line length r0 (see Figure 9).

When the traction phase starts, the kite flies as linelength r increases due to a positive value rref of the line

FIGURE 10 (a) Carousel configuration phases. The same rotor arm is depicted with three subse-quent angular values. The passive phase starts when the rotor arm reaches the angular position�0, and lasts until the rotation angle �3 is reached. To maneuver the kite to a suitable position tobegin the traction phase (highlighted in blue), the passive phase is divided into 3 subphases (gray,orange, and green) delimited by rotation angles �1 and �2. (b) Kite trajectory with carousel config-uration. The kite follows figure-eight orbits, which maximize its speed during the traction phase(green), while during the passive phase (red) the airfoil speed is very low to reduce drag forces.The kite steering unit follows a circular trajectory at ground height, with radius R.

Passive Phaseand Right WindChange

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DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 33

Page 10: Electricity Generation Using Kites

speed reference provided by the local motor controller.Since a traction force Fc is created on the kite lines, thesystem generates mechanical power. The predictivecontrol law computes the line angle ψ (see Figure 8) inorder to vary Fc and thus optimize the aerodynamicbehavior of the kite for energy generation. The lineangle ψ is obtained by varying �l according to (13) byimposing a setpoint on the desired line length achievedby the local motor controller.

The value of the reference line speed rref is chosen as acompromise between obtaining high traction force action

and high line winding speed. Basically, the stronger thewind, the higher the value of rref that can be set whileobtaining high force values. The control system objectivein the traction phase is to maximize the energy generatedduring the prediction interval [tk, tk + TP] . Since theinstantaneous generated mechanical power isP(t) = r(t)Fc(t), MPC minimizes the cost function

J(tk) = −∫ tk+Tp

tk

r(τ)Fc(τ)dτ . (20)

The traction phase ends when the length of the lines reach-es a given value r and the passive phase begins.

The passive phase is divided into three subphases. Inthe first subphase, the line speed r(t) is controlled tosmoothly decrease toward zero. The control objective is tomove the kite into a zone with low values of θ and highvalues of |φ| (see Figure 7), where the effective wind speed�We and force Fc are low and the kite can be recovered with

low energy expense. Then, in the second subphase, r(t) iscontrolled to smoothly decrease from zero to a negativevalue, which provides a compromise between highrewinding speed and low force Fc . During this passivesubphase, the control objective is to minimize the energyspent to rewind the lines. This second subphase endswhen the line length r reaches the desired minimum value.In the third passive subphase, r(t) is controlled to smooth-ly increase toward zero from the previous negative set-point. The control objective is to move the kite in thetraction phase starting zone. The passive phase ends whenthe starting conditions for the traction phase are reached.

Carousel Configuration ControllerIn the carousel configuration (see figures 4 and 10), thetorque Tc given by the carousel motor/generator is such

34 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007

FIGURE 11 Simulation results for the yo-yo configuration. Kite trajec-tories are reported during the traction (green) and passive (red)phases of a complete yo-yo configuration cycle in the presence ofwind turbulence. Note that the behavior is similar to Figure 9 despitethe turbulence.

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Y (m) X (m)

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m) Traction

Phase

Passive Phase

KSU

FIGURE 12 Simulated power obtained with the yo-yo configuration. Acomplete cycle is considered in the presence of wind turbulence.The instantaneous course of the generated power during the trac-tion phase (green) is reported together with the power spent for thekite recovery in the passive phase (red). The mean value of thepower generated during the cycle, which is represented by adashed line, is 11.8 kW. The corresponding generated energy is2613 kJ per cycle.

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FIGURE 13 Line speed reference imposed during a completecarousel cycle. The commanded line speed r (t) is chosen on thebasis of simulation data to increase the mean generated power andto ensure that the lengths of the lines at the beginning of each cycleare the same.

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Page 11: Electricity Generation Using Kites

that the rotor moves at the constant reference angularspeed �ref , which is chosen to optimize the net energygenerated in the cycle. Since the angular speed is constant,each kite can be controlled independently, provided thatthe lines never collide. Thus, a single kite is considered inthe following. The traction phase begins at the rotor angu-lar position � = �3, where the nominal wind direction issuch that the kite can pull the rotor arm [see Figure 10(a)].A suitable trajectory for the line speed r during the tractionphase is set to further increase generated power. Recallingthat mechanical power obtained at each instant is the sumof the effects given by line unrolling and rotor movement,MPC minimizes the cost function

J(tk) = −∫ tk+Tp

tk

r(τ)Fc(τ) + �(τ)Tgen(τ)dτ . (21)

When the rotor arm reaches the angle �0, the kite canno longer pull the carousel, and the traction phase ends.Then, the passive phase starts, and the electric generatorlinked to the rotor acts as a motor to drag the carouselbetween angles �0 and �3. Meanwhile, the kite is movedto a suitable position for initiating the next traction phase.

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 35

FIGURE 16 Power generated with the carousel configuration. Two com-plete cycles are considered in the presence of wind turbulence. Theinstantaneous course of the generated power during the traction phas-es (green) is reported together with the power required for the kiterecovery in the passive phases (red). Note the nearly null values ofenergy usage during the passive phases. The mean value of the powergenerated during the two cycles is 621 kW and is represented by adashed line. The corresponding generated energy is 234 MJ per cycle.

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MeanGeneratedPower

Traction Phase

Passive Phase Passive Phase

Traction Phase

Carousel Angle Θ (°)FIGURE 15 Figure-eight kite orbits during the traction phase for thecarousel configuration. Such orbits are imposed by means of suit-able constraints on the angles θ and φ to avoid line wrapping.

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300

−360−340−320−300−280−260−240120130140150160170180190

X (m)

Y (m)

Z (

m)

FIGURE 14 Simulation results for the carousel configuration. Kite and kite steering unit trajectories are reported during traction (green) andpassive (red) phases related to two complete cycles in the presence of turbulence. Note that, despite the turbulence, the trajectories showgood repeatability.

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Page 12: Electricity Generation Using Kites

The passive phase is divided into three subphases.Transitions between subphases are marked by suitablevalues �1 and �2 of the rotor angle [see Figure 10(a)],which are chosen to minimize the total energy spent dur-

ing the passive phase. In the first subphase, the controlobjective is to move each kite to a zone with a low valueof θ [see figures 7 and 10(b)], where the effective windspeed �We and pulling force component tangential to thecarousel Fc sin θ sin φ are much lower. At � = �1, the sec-ond passive subphase begins, where the objective is tochange the kite angular position φ toward φI to begin thetraction phase. At � = �2 , the third passive subphasebegins, where the control objective is to increase the kiteangle θ toward θII to prepare the generator for the sub-squent traction phase. For details, see [7].

SIMULATION RESULTSSimulations of the KiteGen system were performed usingthe wind speed model

Wx(Z) ={

0.04Z + 8 m/s, if Z ≤ 100 m,

0.0171(Z − 100) + 12 m/s, if Z > 100 m.

(22)

The nominal wind speed is 8 m/s at 0 m altitude, whilethe wind speed grows linearly to 12 m/s at 100 m altitudeand up to 17.2 m/s at 300 m altitude. Moreover, windturbulence �Wt is introduced, with uniformly distributedrandom components along the inertial axes (X, Y, Z). Theabsolute value of each component of �Wt ranges from 0m/s to 3 m/s, which corresponds to 36% of the nominalwind speed at 100 m altitude.

Yo-Yo ConfigurationFor simulation, we consider a yo-yo configuration similarto the physical prototype. The numerical values of the kite

36 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007

TABLE 1 Model and control parameters of the simulated yo-yo configuration. Note, in particular, the smallcharacteristic area and low aerodynamic efficiency.

Symbol Numeric Value Description and Units

m 2.5 Kite mass (kg) A 5 Characteristic area (m2) ρ 1.2 Air density (kg/m3) CL 1.2 Lift coefficient CD 0.15 Drag coefficient E = CL

CD8 Aerodynamic efficiency

r 1.5 Traction phase reference for r (m/s)

r −2.5 Passive phase reference for r (m/s)

Tc 0.1 Sample time (s) Nc 1 Control horizon Np 25 Prediction horizon

TABLE 2 State and input constraints and cycle starting andending conditions for the simulated yo-yo configuration.The traction phase starts when θ ≥ θ I , |φ − φI | ≤ 5◦ , andr < r I . The passive phase starts when r > r . State andinput constraints are imposed throughout the cycle.

Constraint Definition Constraint Description

θ I = 40◦ Traction phase starting conditionsφ I = 0◦

r I = 105 mr = 290 m Maximum line length|θ(t)| ≤ 85◦ State constraint|ψ(t)| ≤ 4◦ Input constraints|ψ(t)| ≤ 20◦/s

TABLE 3 Model and control parameters for the carouselconfiguration. Despite the low aerodynamic efficiency, thisstructure can generate a significant amount of energy asshown by the results reported in Figure 16.

Symbol Numeric Value Description and Units

m 50 Kite mass (kg)A 100 Characteristic area (m2)Jz 9108 Rotor moment of inertia

(kg-m2)R 300 Rotor radius (m)ρ 1.2 Air density (kg/m3)CL 1.2 Lift coefficientCD 0.15 Drag coefficientE = CL

CD8 Aerodynamic efficiency

�ref 0.16 Reference � (rev/min)Tc 0.2 Sample time (s)Nc 1 Control horizon (steps)Np 5 Prediction horizon (steps)

TABLE 4 Objectives and starting conditions for the cyclephases and state and input constraints for the carouselconfiguration. In the passive phase, the controller isdesigned to drive θ to θI during the first subphase, φ to φI

during the second subphase, and θ to θI I during the thirdsubphase. These values are chosen to minimize the energyused to return the kite to its position at the beginning of thetraction phase. In particular, small values of θ and φcorrespond to zones with low values of the effective windspeed and the tangential component of the pulling force Fc

[see (14)]. State and input constraints are imposedthroughout the cycle.

Constraint Definition Constraint Description

�0 = 35◦ Passive phase starting conditionθI = 20◦ First passive subphase objective�1 = 135◦ Second passive subphase starting conditionφI = 140◦ Third passive subphase objective�2 = 150◦ Third passive subphase starting conditionθI I = 50◦ Third passive subphase objective�3 = 165◦ Traction phase starting condition|θ(t)| ≤ 85◦ State constraint|ψ(t)| ≤ 3◦ Input constraints|ψ(t)| ≤ 20◦/s

Page 13: Electricity Generation Using Kites

model and control parameters arereported in Table 1, while Table 2contains the state values for thestart and end conditions of eachphase as well as the values of thestate and input constraints.

Figure 11 shows the trajectory ofthe kite, while the power generatedduring the cycle is reported in Fig-ure 12. The mean power is 11.8 kW,which corresponds to energy gener-ation of 2613 kJ per cycle.

Carousel ConfigurationA carousel with a single KSU isconsidered. The model and con-trol parameters employed arereported in Table 3, while Table 4contains the start and end condi-tions for each phase, as well as thevalues of the state and input con-straints. The line speed during thecycle is reported in Figure 13. Thisreference trajectory is chosen onthe basis of the previous simula-tion to maximize the mean generated power and toensure that the length of the lines at the beginning ofeach cycle is the same.

Figure 14 shows the trajectories of the kite and thecontrol unit during two full cycles in the presence of ran-dom wind disturbances. Figure 15 depicts some orbitstraced by the kite during the traction phase, while thepower generated during the two cycles is reported inFigure 16. The mean power is 621 kW, and the generatedenergy is 234 MJ per cycle. Figure 17 depicts the courseof the effective wind speed | �We| (see the section “KiteGenerator Models” for details). It can be noted that dur-ing the traction phase the mean effective wind speed isabout 14 times greater than the tangential speed of therotor connected to the generator, which is 18 km/h.Since the fixed coordinate system (X, Y, Z) is defined onthe basis of the nominal wind direction, a measurablechange of the latter can be overcome by rotating thewhole coordinate system (X, Y, Z), thus obtaining thesame performance without changing either the controlsystem parameters or the starting conditions of the vari-ous phases.

ACKNOWLEDGMENTSKiteGen project is partially supported by RegionePiemonte under the Project “Controllo di aquiloni dipotenza per la generazione eolica di energia” and by Min-istero dell’Università e della Ricerca of Italy under theNational Project “Advanced control and identificationtechniques for innovative applications.”

REFERENCES[1] “Renewables 2005: Global status report” Renewable Energy Policy Net-work, Worldwatch Institute, Wash. D.C., 2005 [Online]. Available:http://www.REN21.net [2] M. Ippolito, “Smart control system exploiting the characteristics of gener-ic kites or airfoils to convert energy,” European patent 02840646, Dec. 2004.[3] M. Milanese and M. Ippolito “Automatic control system and process forthe flight of kites,” International Patent PCT/IT2007/00325, May 2007.[4] M. Canale, L. Fagiano, M. Ippolito, and M. Milanese, “Control of tetheredairfoils for a new class of wind energy generator,” in Proc. 45th IEEE Conf.Decision and Control, San Diego, CA, pp. 2006, 4020–4026.[5] B. Houska and M. Diehl, “Optimal control for power gnerating kites,” inProc. 9th European Control Conf., Kos, Greece, 2007, pp. 3560–3567.[6] A.R. Podgaets and W.J. Ockels, “Flight control of the high altitude windpower system,” in Proc. 7th Conf. Sustainable Applications Tropical IslandStates, Cape Canaveral, FL, 2007, pp. 125–130.[7] M. Canale, L. Fagiano, M. Milanese, and M. Ippolito, “KiteGen project:Control as key technology for a quantum leap in wind energy generators,”in Proc. 26th American Control Conf., New York, 2007, pp. 3522–3528.[8] A. Betz, Introduction to the Theory of Flow Machines. New York: Pergamon, 1966.[9] M.L. Loyd, “Crosswind kite power,” J. Energy, vol. 4, no. 3, pp. 106–111,1980.[10] Danish Association of Wind Industry Web site [Online]. Available:www.windpower.org[11] D.Q. Mayne, J.B. Rawlings, C.V. Rao, and P.O.M. Scokaert, “Con-strained model predictive control: Stability and optimality,” Automatica,vol. 36, pp. 789–814, 2000. [12] M. Canale and M. Milanese, “FMPC: A fast implementation of modelpredictive control,” in Proc. 16th IFAC World Congress, Prague, Czech Repub-lic, July 2005.[13] M. Canale, L. Fagiano, and M. Milanese, “Fast implementation of pre-dictive controllers using SM methodologies,” in Proc. 46th IEEE Conf. Deci-sion and Control, New Orleans, LA, 2007. [14] M. Milanese and C. Novara, “Set membership identification of nonlinearsystems,” Automatica, vol. 40, pp. 957–975, 2004. [15] M. Milanese and C. Novara, “Structured set membership identification ofnonlinear systems with application to vehicles with controlled suspensions,”Control Eng. Practice, vol. 15, pp. 1–16, 2007.[16] K. Hsu, M. Milanese, C. Novara, and K. Poolla, “Nonlinear virtual

DECEMBER 2007 « IEEE CONTROL SYSTEMS MAGAZINE 37

FIGURE 17 Simulated effective wind speed for the carousel configuration. The course of | �We|during the traction subphases (green) and the passive subphases (red) is related to two com-plete carousel cycles. The average values are 250 km/h during the traction phase and 85 km/hduring the passive phase.

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sensors design from data,” in Proc. IFAC Symp. System Identification (SYSID),Newcastle, Australia, pp. 576–581, 2006.[17] K. Hsu, M. Milanese, C. Novara, and K. Poolla, “Filter design from data:Direct vs. two-step approaches,” in Proc. 25th American Control Conf., Min-neapolis, MN, 2006, pp. 1606–1611.[18] M. Diehl, “Real-time optimization for large scale nonlinear processes,”Ph.D. dissertation, University of Heidelberg, Germany, 2001 [Online]. Avail-able: http://www.iwr.uni-heidelberg.de/~Moritz.Diehl/DISSERTATION/diehl_diss.pdf

AUTHOR INFORMATIONMassimo Canale received the Laurea degree in electronicengineering (1992) and the Ph.D. in systems engineering(1997), both from the Politecnico di Torino, Italy. From1997 to 1998, he worked as a software engineer in the R&Ddepartment of Comau Robotics, Italy. Since 1998, he hasbeen an assistant professor in the Dipartimento di Auto-matica e Informatica of the Politecnico di Torino. Hisresearch interests include robust control, model predictivecontrol, set membership approximation, and application toautomotive and aerospace problems.

Lorenzo Fagiano received the master’s degree in auto-motive engineering in 2004 from Politecnico di Torino,Italy. In 2005 he worked at Centro Ricerche Fiat, Italy, inthe active vehicle systems area. Since January 2006 he hasbeen a Ph.D. student at Politecnico di Torino. His mainresearch interests include constrained robust and nonlinearcontrol and set membership theory for control purposes,applied to vehicle stability control and the KiteGen project.

Mario Milanese ([email protected]) graduat-ed in electronic engineering from the Politecnico di Torino,Torino, Italy, in 1967. Since 1980, he has been a full profes-sor of system theory at Politecnico di Torino. From 1982 to1987, he was head of the Dipartimento di Automatica eInformatica at the Politecnico di Torino. His research inter-ests include identification, prediction, and control ofuncertain systems with applications to biomedical, auto-motive, aerospace, financial, environmental, and energyproblems. He is the author of more than 200 papers ininternational journals and conference proceedings.

38 IEEE CONTROL SYSTEMS MAGAZINE » DECEMBER 2007

To conclude the column, I wouldlike to mention that being the VPMAof this society for two years has beena wonderful experience, whichallowed me to interact with persons Iinitially knew just by name andwhom I now regard as real friends. Inparticular, I would like to mentionRick Middleton, the vice president forconference activities and past VPMA,

and Faryar Jabbari, the StudentActivities Chair. Their preciousadvice, together with their energyand their wonderful temperament,has made my job not only easier butoften very pleasant and enjoyable!

Finally, I find the chance to men-tion that in January 2008, I will stepdown, and Claire Tomlin will be tak-ing over the role of vice president for

member activities. Claire is not onlyan excellent scientist, as the hugenumber of awards she has alreadyreceived despite her young age testi-fies, but also an energetic and reliableperson. So, I wish her good luck, hav-ing no doubts that she will do a greatjob as VPMA.

Maria Elena Valcher